arXiv:1511.08380v2 [hep-ex] 18 Feb 2016
Measurements of Absolute Hadronic Branching Fractions of the
Λ
cBaryon
M. Ablikim1, M. N. Achasov9,e, X. C. Ai1, O. Albayrak5, M. Albrecht4, D. J. Ambrose44, A. Amoroso49A,49C, F. F. An1,Q. An46,a, J. Z. Bai1, R. Baldini Ferroli20A, Y. Ban31, D. W. Bennett19, J. V. Bennett5, M. Bertani20A, D. Bettoni21A, J. M. Bian43, F. Bianchi49A,49C, E. Boger23,c, I. Boyko23, R. A. Briere5, H. Cai51, X. Cai1,a, O. Cakir40A, A. Calcaterra20A,
G. F. Cao1, S. A. Cetin40B, J. F. Chang1,a, G. Chelkov23,c,d, G. Chen1, H. S. Chen1, H. Y. Chen2, J. C. Chen1, M. L. Chen1,a, S. J. Chen29, X. Chen1,a, X. R. Chen26, Y. B. Chen1,a, H. P. Cheng17, X. K. Chu31, G. Cibinetto21A, H. L. Dai1,a, J. P. Dai34, A. Dbeyssi14, D. Dedovich23, Z. Y. Deng1, A. Denig22, I. Denysenko23, M. Destefanis49A,49C, F. De Mori49A,49C, Y. Ding27, C. Dong30, J. Dong1,a, L. Y. Dong1, M. Y. Dong1,a, Z. L. Dou29, S. X. Du53, P. F. Duan1, E. E. Eren40B, J. Z. Fan39, J. Fang1,a, S. S. Fang1, X. Fang46,a, Y. Fang1, R. Farinelli21A,21B, L. Fava49B,49C, O. Fedorov23,
F. Feldbauer22, G. Felici20A, C. Q. Feng46,a, E. Fioravanti21A, M. Fritsch14,22, C. D. Fu1, Q. Gao1, X. L. Gao46,a, X. Y. Gao2, Y. Gao39, Z. Gao46,a, I. Garzia21A, K. Goetzen10, L. Gong30, W. X. Gong1,a, W. Gradl22, M. Greco49A,49C, M. H. Gu1,a, Y. T. Gu12, Y. H. Guan1, A. Q. Guo1, L. B. Guo28, Y. Guo1, Y. P. Guo22, Z. Haddadi25, A. Hafner22, S. Han51, X. Q. Hao15, F. A. Harris42, K. L. He1, T. Held4, Y. K. Heng1,a, Z. L. Hou1, C. Hu28, H. M. Hu1, J. F. Hu49A,49C, T. Hu1,a, Y. Hu1, G. S. Huang46,a, J. S. Huang15, X. T. Huang33, Y. Huang29, T. Hussain48, Q. Ji1, Q. P. Ji30, X. B. Ji1, X. L. Ji1,a,
L. W. Jiang51, X. S. Jiang1,a, X. Y. Jiang30, J. B. Jiao33, Z. Jiao17, D. P. Jin1,a, S. Jin1, T. Johansson50, A. Julin43, N. Kalantar-Nayestanaki25, X. L. Kang1, X. S. Kang30, M. Kavatsyuk25, B. C. Ke5, P. Kiese22, R. Kliemt14, B. Kloss22, O. B. Kolcu40B,h, B. Kopf4, M. Kornicer42, W. Kuehn24, A. Kupsc50, J. S. Lange24,a, M. Lara19, P. Larin14, C. Leng49C,
C. Li50, Cheng Li46,a, D. M. Li53, F. Li1,a, F. Y. Li31, G. Li1, H. B. Li1, J. C. Li1, Jin Li32, K. Li13, K. Li33, Lei Li3, P. R. Li41, Q. Y. Li33, T. Li33, W. D. Li1, W. G. Li1, X. L. Li33, X. M. Li12, X. N. Li1,a, X. Q. Li30, Z. B. Li38, H. Liang46,a, Y. F. Liang36, Y. T. Liang24, G. R. Liao11, D. X. Lin14, B. J. Liu1, C. X. Liu1, D. Liu46,a, F. H. Liu35, Fang Liu1, Feng Liu6,
H. B. Liu12, H. H. Liu1, H. H. Liu16, H. M. Liu1, J. Liu1, J. B. Liu46,a, J. P. Liu51, J. Y. Liu1, K. Liu39, K. Y. Liu27, L. D. Liu31, P. L. Liu1,a, Q. Liu41, S. B. Liu46,a, X. Liu26, Y. B. Liu30, Z. A. Liu1,a, Zhiqing Liu22, H. Loehner25, X. C. Lou1,a,g, H. J. Lu17, J. G. Lu1,a, Y. Lu1, Y. P. Lu1,a, C. L. Luo28, M. X. Luo52, T. Luo42, X. L. Luo1,a, X. R. Lyu41,
F. C. Ma27, H. L. Ma1, L. L. Ma33, Q. M. Ma1, T. Ma1, X. N. Ma30, X. Y. Ma1,a, Y. M. Ma33, F. E. Maas14, M. Maggiora49A,49C, Y. J. Mao31, Z. P. Mao1, S. Marcello49A,49C, J. G. Messchendorp25, J. Min1,a, R. E. Mitchell19,
X. H. Mo1,a, Y. J. Mo6, C. Morales Morales14, N. Yu. Muchnoi9,e, H. Muramatsu43, Y. Nefedov23, F. Nerling14, I. B. Nikolaev9,e, Z. Ning1,a, S. Nisar8, S. L. Niu1,a, X. Y. Niu1, S. L. Olsen32, Q. Ouyang1,a, S. Pacetti20B, Y. Pan46,a, P. Patteri20A, M. Pelizaeus4, H. P. Peng46,a, K. Peters10, J. Pettersson50, J. L. Ping28, R. G. Ping1, R. Poling43, V. Prasad1,
H. R. Qi2, M. Qi29, S. Qian1,a, C. F. Qiao41, L. Q. Qin33, N. Qin51, X. S. Qin1, Z. H. Qin1,a, J. F. Qiu1, K. H. Rashid48, C. F. Redmer22, M. Ripka22, G. Rong1, Ch. Rosner14, X. D. Ruan12, V. Santoro21A, A. Sarantsev23,f, M. Savri´e21B,
K. Schoenning50, S. Schumann22, W. Shan31, M. Shao46,a, C. P. Shen2, P. X. Shen30, X. Y. Shen1, H. Y. Sheng1, W. M. Song1, X. Y. Song1, S. Sosio49A,49C, S. Spataro49A,49C, G. X. Sun1, J. F. Sun15, S. S. Sun1, Y. J. Sun46,a, Y. Z. Sun1,
Z. J. Sun1,a, Z. T. Sun19, C. J. Tang36, X. Tang1, I. Tapan40C, E. H. Thorndike44, M. Tiemens25, M. Ullrich24, I. Uman40D, G. S. Varner42, B. Wang30, B. L. Wang41, D. Wang31, D. Y. Wang31, K. Wang1,a, L. L. Wang1, L. S. Wang1, M. Wang33,
P. Wang1, P. L. Wang1, S. G. Wang31, W. Wang1,a, W. P. Wang46,a, X. F. Wang39, Y. D. Wang14, Y. F. Wang1,a, Y. Q. Wang22, Z. Wang1,a, Z. G. Wang1,a, Z. H. Wang46,a, Z. Y. Wang1, T. Weber22, D. H. Wei11, J. B. Wei31, P. Weidenkaff22, S. P. Wen1, U. Wiedner4, M. Wolke50, L. H. Wu1, Z. Wu1,a, L. Xia46,a, L. G. Xia39, Y. Xia18, D. Xiao1, H. Xiao47, Z. J. Xiao28, Y. G. Xie1,a, Q. L. Xiu1,a, G. F. Xu1, L. Xu1, Q. J. Xu13, Q. N. Xu41, X. P. Xu37, L. Yan49A,49C,
W. B. Yan46,a, W. C. Yan46,a, Y. H. Yan18, H. J. Yang34, H. X. Yang1, L. Yang51, Y. X. Yang11, M. Ye1,a, M. H. Ye7, J. H. Yin1, B. X. Yu1,a, C. X. Yu30, J. S. Yu26, C. Z. Yuan1, W. L. Yuan29, Y. Yuan1, A. Yuncu40B,b, A. A. Zafar48, A. Zallo20A, Y. Zeng18, Z. Zeng46,a, B. X. Zhang1, B. Y. Zhang1,a, C. Zhang29, C. C. Zhang1, D. H. Zhang1, H. H. Zhang38, H. Y. Zhang1,a, J. J. Zhang1, J. L. Zhang1, J. Q. Zhang1, J. W. Zhang1,a, J. Y. Zhang1, J. Z. Zhang1, K. Zhang1, L. Zhang1,
X. Y. Zhang33, Y. Zhang1, Y. H. Zhang1,a, Y. N. Zhang41, Y. T. Zhang46,a, Yu Zhang41, Z. H. Zhang6, Z. P. Zhang46, Z. Y. Zhang51, G. Zhao1, J. W. Zhao1,a, J. Y. Zhao1, J. Z. Zhao1,a, Lei Zhao46,a, Ling Zhao1, M. G. Zhao30, Q. Zhao1, Q. W. Zhao1, S. J. Zhao53, T. C. Zhao1, Y. B. Zhao1,a, Z. G. Zhao46,a, A. Zhemchugov23,c, B. Zheng47, J. P. Zheng1,a, W. J. Zheng33, Y. H. Zheng41, B. Zhong28, L. Zhou1,a, X. Zhou51, X. K. Zhou46,a, X. R. Zhou46,a, X. Y. Zhou1, K. Zhu1,
K. J. Zhu1,a, S. Zhu1, S. H. Zhu45, X. L. Zhu39, Y. C. Zhu46,a, Y. S. Zhu1, Z. A. Zhu1, J. Zhuang1,a, L. Zotti49A,49C, B. S. Zou1, J. H. Zou1
(BESIII Collaboration)
1 Institute of High Energy Physics, Beijing 100049, People’s Republic of China 2 Beihang University, Beijing 100191, People’s Republic of China
3 Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China 4 Bochum Ruhr-University, D-44780 Bochum, Germany
5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 6 Central China Normal University, Wuhan 430079, People’s Republic of China
7 China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China
8 COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan 9 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
10GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany 11 Guangxi Normal University, Guilin 541004, People’s Republic of China
13 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China 14 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
15 Henan Normal University, Xinxiang 453007, People’s Republic of China
16 Henan University of Science and Technology, Luoyang 471003, People’s Republic of China 17Huangshan College, Huangshan 245000, People’s Republic of China
18Hunan University, Changsha 410082, People’s Republic of China 19 Indiana University, Bloomington, Indiana 47405, USA
20(A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy
21 (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy 22Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
23 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
24 Justus Liebig University Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany 25 KVI-CART, University of Groningen, NL-9747 AA Groningen, Netherlands
26Lanzhou University, Lanzhou 730000, People’s Republic of China 27Liaoning University, Shenyang 110036, People’s Republic of China 28 Nanjing Normal University, Nanjing 210023, People’s Republic of China
29 Nanjing University, Nanjing 210093, People’s Republic of China 30Nankai University, Tianjin 300071, People’s Republic of China
31 Peking University, Beijing 100871, People’s Republic of China 32Seoul National University, Seoul, 151-747 Korea 33
Shandong University, Jinan 250100, People’s Republic of China 34Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
35 Shanxi University, Taiyuan 030006, People’s Republic of China 36
Sichuan University, Chengdu 610064, People’s Republic of China 37 Soochow University, Suzhou 215006, People’s Republic of China 38Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
39Tsinghua University, Beijing 100084, People’s Republic of China
40(A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey; (C)Uludag University, 16059 Bursa, Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey
41 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 42 University of Hawaii, Honolulu, Hawaii 96822, USA
43 University of Minnesota, Minneapolis, Minnesota 55455, USA 44University of Rochester, Rochester, New York 14627, USA
45 University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China 46 University of Science and Technology of China, Hefei 230026, People’s Republic of China
47 University of South China, Hengyang 421001, People’s Republic of China 48 University of the Punjab, Lahore-54590, Pakistan
49 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy
50 Uppsala University, Box 516, SE-75120 Uppsala, Sweden 51Wuhan University, Wuhan 430072, People’s Republic of China 52Zhejiang University, Hangzhou 310027, People’s Republic of China 53Zhengzhou University, Zhengzhou 450001, People’s Republic of China
a Also at State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, People’s Republic of China
bAlso at Bogazici University, 34342 Istanbul, Turkey
c Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia dAlso at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia
e Also at the Novosibirsk State University, Novosibirsk, 630090, Russia f Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia
g Also at University of Texas at Dallas, Richardson, Texas 75083, USA hAlso at Istanbul Arel University, 34295 Istanbul, Turkey
1 1
We report the first measurement of absolute hadronic branching fractions of Λ+
c baryon at the Λ+
cΛ−c production threshold, in the 30 years since the Λ+c discovery. In total, twelve Cabibbo-favored Λ+
c hadronic decay modes are analyzed with a double-tag technique, based on a sample of 567 pb−1 of e+
fitter is utilized to improve the measured precision. Among the measurements for twelve Λ+ c decay modes, the branching fraction for Λ+
c → pK−π+ is determined to be (5.84 ± 0.27 ± 0.23)%, where the first uncertainty is statistical and the second is systematic. In addition, the measurements of the branching fractions of the other eleven Cabibbo-favored hadronic decay modes are significantly improved.
PACS numbers: 14.20.Lq, 13.30.Eg, 13.66.Bc
Charmed baryon decays provide crucial information for the study of both strong and weak interactions. Hadronic decays of Λ+
c, the lightest charmed baryon
with quark configuration udc, provide important input to Λb physics as Λb decays dominantly to Λ+c [1, 2].
Improved measurements of the Λ+
c hadronic decays can
be used to constrain fragmentation functions of charm and bottom quarks by counting inclusive heavy flavor baryons [3]. Most Λ+
c branching fractions (BF) have until
now been obtained by combining measurements of ratios with a single branching fraction of the golden reference mode Λ+
c → pK
−π+, thus introducing strong
correla-tions and compounding uncertainties. The experimen-tally averaged BF, B(Λ+
c → pK
−
π+) = (5.0 ± 1.3)% [4],
has large uncertainty due to the introduction of mod-el assumptions on Λ+
c inclusive decays in these
mea-surements [5]. Recently, the Belle experiment reported B(Λ+
c → pK
−π+) = (6.84 ± 0.24+0.21
−0.27)% with a
preci-sion improved by a factor of 5 over previous results [6]. However, most hadronic BFs still have poor precision [4]. In this Letter, we present the first simultaneous determi-nation of multiple Λ+
c absolute BFs.
Our analysis is based on a data sample with an in-tegrated luminosity of 567 pb−1 [7] collected with the BESIII detector [8] at the center-of-mass energy of√s = 4.599 GeV. At this energy, no additional hadrons accom-panying the Λ+
cΛ −
c pairs are produced. Previously, the
Mark III collaboration measured D hadronic BFs at the D ¯D threshold using a double-tag technique, which re-lies on fully reconstructing both D and ¯D decays [9]. This technique obviates the need for knowledge of the luminosity or the production cross section. We em-ploy a similar technique [10] using BESIII data near the Λ+
cΛ −
c threshold, resulting in improved
measure-ments of charge-averaged BFs for twelve Cabibbo-favored hadronic decay modes: Λ+
c → pKS0, pK − π+, pK0 Sπ0, pK0 Sπ+π − , pK− π+π0, Λπ+, Λπ+π0, Λπ+π− π+, Σ0π+,
Σ+π0, Σ+π+π−, and Σ+ω [11]. Throughout the Letter,
charge-conjugate modes are implicitly assumed, unless otherwise stated.
To identify the Λ+ cΛ
−
c signal candidates, we first
recon-struct one Λ−
c baryon [called a single tag (ST)] through
the final states of any of the twelve modes. For a given decay mode j, the ST yield is determined to be
NjST= NΛ+
cΛ−c · Bj· εj, (1) where NΛ+
cΛ−c is the total number of produced Λ
+ cΛ
− c
pairs and εj is the corresponding efficiency. Then we
define double-tag (DT) events as those where the partner Λ+
c recoiling against the Λ −
c is reconstructed in one of the
twelve modes. That is, in DT events, the Λ+ cΛ
−
c event is
fully reconstructed. The DT yield with Λ+c → i (signal
mode) and Λ−
c → j (tagging mode) is
NijDT= NΛ+
cΛ−c · Bi· Bj· εij, (2) where εij is the efficiency for simultaneously
reconstruct-ing modes i and j. Hence, the ratio of the DT yield (NDT
ij ) and ST yield (NjST) provides an absolute
mea-surement of the BF: Bi= NDT ij NST j εj εij . (3)
Because of the large acceptance of the BESIII detec-tor and the low multiplicities of Λc hadronic decays,
εij ≈ εiεj. Hence, the ratio εj/εij is insensitive to most
systematic effects associated with the decay mode j, and a signal BF Bi obtained using this procedure is
near-ly independent of the efficiency of the tagging mode. Therefore, Bi is sensitive to the signal mode efficiency
(εi), whose uncertainties dominate the contribution to
the systematic error from the efficiencies. According to Eqs. (1) and (2), the total DT yield with Λ+
c → i (signal
mode) over the twelve ST modes is determined to be Ni−DT= NΛ+ cΛ−c · X j Bi· Bj· εDTi− , (4) where εDT i− ≡ P jP(Bj·εij)
jBj is the average DT efficiency weighted over the twelve modes.
The BESIII detector is an approximately cylindrically symmetric detector with 93% coverage of the solid an-gle around the e+e−
interaction point (IP). The com-ponents of the apparatus, ordered by distance from the IP, are a 43-layer small-cell main drift chamber (MDC), a time-of-flight (TOF) system based on plastic scintilla-tors with two layers in the barrel region and one layer in the end-cap region, a 6240-cell CsI(Tl) crystal electro-magnetic calorimeter (EMC), a superconducting solenoid magnet providing a 1.0 T magnetic field aligned with the beam axis, and resistive-plate muon-counter layers inter-leaved with steel. The momentum resolution for charged tracks in the MDC is 0.5% for a transverse momen-tum of 1 GeV/c. The energy resolution in the EMC is 2.5% in the barrel region and 5.0% in the end-cap re-gion for 1 GeV photons. Particle identification (PID) for charged tracks combines measurements of the energy de-posit dE/dx in MDC and flight time in TOF and forms likelihoods L(h) (h = p, K, π) for a hadron h hypothe-sis. More details about the BESIII detector are provided elsewhere [8].
High-statistics Monte Carlo (MC) simulations of e+e−
annihilations are used to understand backgrounds and to estimate detection efficiencies. The simulation includes the beam-energy spread and initial-state radiation (ISR) of the e+e−
collisions as simulated with KKMC [12]. The inclusive MC sample consists of Λ+
cΛ −
c events, D(s)
production [13], ISR return to lower-mass ψ states, and continuum processes e+e−
→ q¯q (q = u, d, s). Decay modes as specified in the Particle Data Group summary (PDG) [4] are modeled with EVTGEN [14]. For the MC production of e+e−
→ Λ+ cΛ
−
c, the observed cross
sec-tions are taken into account, and phase-space-generated Λ+
c decays are reweighted according to the observed
be-haviors in data. All final tracks and photons are fed into a GEANT4-based [15] detector simulation package.
Charged tracks detected in the MDC must satisfy | cos θ| < 0.93 (where θ is the polar angle with respect to the beam direction) and have a distance of closest ap-proach to the IP of less than 10 cm along the beam axis and less than 1 cm in the perpendicular plane, except for those used for reconstructing K0
S and Λ decays. Tracks
are identified as protons when the PID determines this hypothesis to have the greatest likelihood (L(p) > L(K) and L(p) > L(π)), while charged kaons and pions are dis-criminated based on comparing the likelihoods for these two hypotheses (L(K) > L(π) or L(π) > L(K)).
Showers in the EMC not associated with any charged track are identified as photon candidates after fulfill-ing the followfulfill-ing requirements. The deposited ener-gy is required to be larger than 25 MeV in the bar-rel (| cos θ| < 0.8) region and 50 MeV in the end-cap region(0.84 < | cos θ| < 0.92). To suppress electronic noise and showers unrelated to the event, the EMC time deviation from the event start time is required to be with-in (0, 700) ns. The π0 candidates are reconstructed from
photon pairs, and their invariant masses are required to satisfy 115 < M (γγ) < 150 MeV/c2. To improve
momen-tum resolution, a mass-constrained fit to the π0nominal
mass is applied to the photon pairs and the resulting energy and momentum of the π0 are used for further
analysis.
Candidates for K0
S and Λ are formed by combining
two oppositely charged tracks into the final states π+π−
and pπ−. For these two tracks, their distances of
clos-est approaches to the IP must be within ±20 cm along the beam direction. No distance constraints in the trans-verse plane are required. The charged π is not subject-ed to the PID requirements describsubject-ed above, while pro-ton PID is implemented in order to improve signal sig-nificance. The two daughter tracks are constrained to originate from a common decay vertex by requiring the χ2 of the vertex fit to be less than 100. Furthermore,
the decay vertex is required to be separated from the IP by a distance of at least twice the fitted vertex res-olution. The fitted momenta of the π+π−
and pπ−
are used in the further analysis. We impose requirements 487 < M (π+π−
) < 511 MeV/c2 and 1111 < M (pπ−
) < 1121 MeV/c2 to select K0
S and Λ signal candidates,
re-) 2 c (GeV/ BC M 2c Events/2.0 MeV/ 1000 2000 3000 0 S pK 2.26 2.28 2.3 200 400 600 Λπ+ 2.26 2.28 2.3 100 200 300 0π0 S pK 2.26 2.28 2.3 100 200 0π+π -S pK 1000 2000 3000 -π+ pK 2.26 2.28 2.3 200 400 600 Λπ+π0 2.26 2.28 2.3 100 200 300 + π -π + π Λ 2.26 2.28 2.3 100 200 Σ+π0 1000 2000 3000 0 π + π -pK 2.26 2.28 2.3 200 400 600 Σ+π+π -2.26 2.28 2.3 100 200 300 + π 0 Σ 2.26 2.28 2.3 100 200 Σ+ω
FIG. 1. Fits to the ST MBC distributions in data for the different decay modes. Points with error bars are data, solid lines are the sum of the fit functions, and dashed lines are the background shapes.
spectively, which are within about 3 standard deviations from their nominal masses. To form Σ0, Σ+ and ω
can-didates, requirements on the invariant masses of 1179 < M (Λγ) < 1203 MeV/c2, 1176 < M (pπ0) < 1200 MeV/c2
and 760 < M (π+π−π0) < 800 MeV/c2, are imposed.
When we reconstruct the decay modes pK0 Sπ0,
pK0 Sπ+π
−
and Σ+π+π−
, possible backgrounds from Λ → pπ− in the final states are rejected by requiring M (pπ−)
outside the range (1110, 1120) MeV/c2. In addition, for
the mode pK0
Sπ0, candidate events within the range
1170 < M (pπ0) < 1200 MeV/c2are excluded to suppress
Σ+backgrounds. To remove K0
Scandidates in the modes
Λπ+π−π+, Σ+π0 and Σ+π+π−, masses of any pairs of
π+π− and π0π0are not allowed to fall in the range (480,
520) MeV/c2.
To discriminate Λc candidates from background, two
variables reflecting energy and momentum conservation are used. First, we calculate the energy difference, ∆E ≡ E − Ebeam, where E is the total measured
en-ergy of the Λc candidate and Ebeam is the average value
of the e+ and e−
beam energies. For each tag mode, candidates are rejected if they fail the ∆E requirements in Table I, which correspond to about 3 times the reso-lutions. Second, we define the beam-constrained mass MBC of the Λc candidates by substituting the
beam-energy Ebeam for the energy E of the Λc candidates,
MBCc2 ≡ pEbeam2 − p2c2, where p is the measured Λc
momentum in the center-of-mass system of the e+e−
col-lision. Figure 1 shows the MBCdistributions for the ST
samples, where evident Λcsignals peak at the nominal Λc
mass position (2286.46±0.14) MeV/c2[4]. The MC
sim-ulations show that peaking backgrounds and cross feeds among the twelve ST modes are negligible.
TABLE I. Requirement on ∆E, ST yields, DT yields and detection efficiencies for each of the decay modes. The un-certainties are statistical only. The quoted efficiencies do not include any subleading BFs.
Mode ∆E (MeV) NjST εj(%) Ni−DT εDTi−(%)
pKS0 (−20, 20) 1243 ± 37 55.9 97 ± 10 16.6 pK−π+ (−20, 20) 6308 ± 88 51.2 420 ± 22 14.1 pKS0π 0 (−30, 20) 558 ± 33 20.6 47 ± 8 6.8 pK0 Sπ+π− (−20, 20) 485 ± 29 21.4 34 ± 6 6.4 pK−π+π0 (−30, 20) 1849 ± 71 19.6 176 ± 14 7.6 Λπ+ (−20, 20) 706 ± 27 42.2 60 ± 8 12.7 Λπ+ π0 (−30, 20) 1497 ± 52 15.7 101 ± 13 5.4 Λπ+ π−π+ (−20, 20) 609 ± 31 12.0 53 ± 7 3.6 Σ0π+ (−20, 20) 522 ± 27 29.9 38 ± 6 9.9 Σ+ π0 (−50, 30) 309 ± 24 23.8 25 ± 5 8.0 Σ+ π+π− (−30, 20) 1156 ± 49 24.2 80 ± 9 8.1 Σ+ ω (−30, 20) 157 ± 22 9.9 13 ± 3 3.8
We perform unbinned extended maximum likelihood fits to the MBC distributions to obtain the ST yields,
as illustrated in Fig. 1. In each fit, the signal shape is derived from MC simulations of the signal ST modes convolved with a Gaussian function to account for imper-fect modeling of the detector resolution and beam-energy spread. The parameters of the Gaussians are allowed to vary in the fits. Backgrounds for each mode are described with the ARGUS function [16]. The resultant ST yields in the signal region 2276 < MBC< 2300 MeV/c2and the
corresponding detection efficiencies are listed in Table I. In the signal candidates of the twelve ST modes, a spe-cific mode Λ+
c → i is formed from the remaining tracks
and showers recoiling against the ST Λ−
c. We combine
the DT signal candidates over the twelve ST modes and plot the distributions of the MBCvariable in Fig. 2. We
follow the same fit strategy as in the ST samples to es-timate the total DT yield NDT
i− in Eq. (4), except that
the DT signal shapes are derived from the DT signal MC samples and convolved with the Gaussian function. The parameters of the Gaussians are also allowed to vary in the fits. The extracted DT yields are listed in Table I. The 12 × 12 DT efficiencies εij are evaluated based on
the DT signal MC samples, in order to extract the BFs. Main sources of systematic uncertainties related to the measurement of BFs include tracking, PID, reconstruc-tion of intermediate states and intermediate BFs. For the ∆E and MBC requirements, the uncertainties are
negligible, as we correct resolutions in MC samples to accord with those in data. Uncertainties associated with the efficiencies of the tracking and PID of charged par-ticles are estimated by studying a set of control sam-ples of e+e−
→ π+π+π−π−, K+K−π+π− and p¯pπ+π−
based on data taken at energies above √s = 4.0 GeV. An uncertainty of 1.0% is assigned to each π0due to the
reconstruction efficiency. The uncertainties of detecting K0
S and Λ are determined to be 1.2% and 2.5%,
respec-) 2 c (GeV/ BC M 2c Events/1.0 MeV/ 50 100 pK0S 2.26 2.28 2.3 10 20 Λπ+ 2.26 2.28 2.3 5 10 15 20 0π0 S pK sig_mBC_3 2.26 2.28 2.3 5 10 15 -π + π 0 S pK 50 100 π+ -pK 2.26 2.28 2.3 10 20 Λπ+π0 2.26 2.28 2.3 5 10 15 20 + π -π + π Λ sig_mBC_62 2.26 2.28 2.3 5 10 15 0 π + Σ 50 100 pK-π+π0 2.26 2.28 2.3 10 20 Σ+π+π -2.26 2.28 2.3 5 10 15 20 + π 0 Σ sig_mBC_64 2.26 2.28 2.3 5 10 15 ω + Σ
FIG. 2. Fits to the DT MBCdistributions in data for different signal modes. Points with error bars are data, solid lines are the sum of fit functions, and dashed lines are background shapes.
TABLE II. Summary of systematic uncertainties, in percent. The total numbers are derived from the least-squares fit, by taking into account correlations among different modes.
Source Tracking PID K0 S Λ π0 Signal MC Quoted Total model stat. BFs pK0 S 1.3 0.3 1.2 0.2 0.4 0.1 2.0 pK−π+ 2.5 3.2 0.2 3.9 pKS0π 0 1.1 1.6 1.2 1.0 1.0 0.5 0.1 2.7 pK0 Sπ+π− 2.8 5.4 1.2 0.5 0.5 0.1 5.9 pK−π+π0 3.3 5.8 1.0 2.0 0.5 6.6 Λπ+ 1.0 1.0 2.5 0.5 0.5 0.8 2.4 Λπ+π0 1.0 1.0 2.5 1.0 0.6 0.6 0.8 2.7 Λπ+ π−π+ 3.0 3.0 2.5 0.8 0.8 0.8 4.7 Σ0 π+ 1.0 1.0 2.5 1.7 0.7 0.8 2.4 Σ+π0 1.3 0.3 2.0 1.7 0.8 0.1 2.5 Σ+ π+π− 3.0 3.7 1.0 0.8 0.4 0.1 4.7 Σ+ ω 3.0 3.2 2.0 7.1 1.0 0.8 4.5
tively. Reweighting factors for the twelve signal models are varied within their statistical uncertainties obtained from the ST data samples. Deviations of the resultant ef-ficiencies are taken into account in systematic uncertain-ties. Systematic uncertainties due to limited statistics in MC samples are included. Uncertainties on the BFs of intermediate state decays from the PDG [4] are also in-cluded. A summary of systematic uncertainties are given in Table II.
We use a least-squares fitter, which considers statistical and systematic correlations among the different hadronic modes, to obtain the BFs of the twelve Λ+
c decay modes
globally. Details of this fitter are discussed in Ref. [17]. In the fitter, the precisions of the twelve BFs are constrained to a common variable, NΛ+
TABLE III. Comparison of the measured BFs in this work with previous results from PDG [4]. For our results, the first uncertainties are statistical and the second are systematic.
Mode This work (%) PDG (%)
pKS0 1.52 ± 0.08 ± 0.03 1.15 ± 0.30 pK−π+ 5.84 ± 0.27 ± 0.23 5.0 ± 1.3 pKS0π0 1.87 ± 0.13 ± 0.05 1.65 ± 0.50 pKS0π + π− 1.53 ± 0.11 ± 0.09 1.30 ± 0.35 pK−π+π0 4.53 ± 0.23 ± 0.30 3.4 ± 1.0 Λπ+ 1.24 ± 0.07 ± 0.03 1.07 ± 0.28 Λπ+ π0 7.01 ± 0.37 ± 0.19 3.6 ± 1.3 Λπ+ π−π+ 3.81 ± 0.24 ± 0.18 2.6 ± 0.7 Σ0 π+ 1.27 ± 0.08 ± 0.03 1.05 ± 0.28 Σ+ π0 1.18 ± 0.10 ± 0.03 1.00 ± 0.34 Σ+π+π− 4.25 ± 0.24 ± 0.20 3.6 ± 1.0 Σ+ ω 1.56 ± 0.20 ± 0.07 2.7 ± 1.0
(4). In total, there are thirteen free parameters (twelve Bi
and NΛ+
cΛ−c) to be estimated. As peaking backgrounds in ST modes and cross feeds among the twelve ST modes are suppressed to a negligible level, they are not considered in the fit.
The extracted BFs of Λ+
c are listed in Table III; the
cor-relation matrix is available in the Supplemental Material. The total number of Λ+cΛ
−
c pairs produced is obtained to
be NΛ+
cΛ−c = (105.9±4.8±0.5)×10
3. The goodness-of-fit
is evaluated as χ2/ndf = 9.9/(24 − 13) = 0.9.
To summarize, twelve Cabibbo-favored Λ+
c decay rates
are measured by employing a double-tag technique, based on a sample of threshold data at √s = 4.599 GeV col-lected at BESIII. This is the first absolute measurement of the Λ+
c decay branching fractions at the Λ+cΛ − c
pro-duction threshold, in the 30 years since the Λ+
c
discov-ery. A comparison with previous results is presented in Table III. For the golden mode B(pK−π+), our result is
consistent with that in PDG, but lower than Belle’s with a significance of about 2σ. For the branching fractions of
the other modes, the precisions are improved by factors of 3 ∼ 6 compared to the world average values.
The BESIII Collaboration thanks the staff of BEPCII and the IHEP computing center for their strong sup-port. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC) under Contracts No. 11125525, No. 11235011, No. 11275266, No. 11322544, No. 11335008 and No. 11425524; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); the Collaborative Innovation Center for Particles and Interactions (CICPI); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS un-der Contracts No. 11179007, No. U1232201 and No. U1332201; CAS under Contracts No. KJCX2-YW-N29 and No. KJCX2-YW-N45; 100 Talents Program of CAS; National 1000 Talents Program of China; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. Collaborative Research Center CRC-1044; Istituto Nazionale di Fisica Nucleare, Italy; Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) under Contract No. 530-4CDP03; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Natural Science Foundation of China (NSFC) under Contracts No. 11405046 and No. U1332103; Russian Foundation for Basic Research un-der Contract No. 14-07-91152; The Swedish Resarch Council; U. S. Department of Energy under Contracts No. DE-FG02-04ER41291, No. DE-FG02-05ER41374, No. de-sc0012069, and No. DESC0010118; U.S. National Science Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; and WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.
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SUPPLEMENTAL MATERIAL
We present the correlation matrix of the branching fraction fit. In total, there are thirteen correlated items; one NΛ+
TABLE IV. Correlation coefficients among thirteen fit parameters, including both statistical and systematic uncertainties. NΛ+ cΛ−c B(pK 0 S) B(pK−π +) B(pK0 Sπ 0) B(pK0 Sπ +π−) B(pK−π+π0) B(Λπ+) B(Λπ+π0) B(Λπ+π−π+) B(Σ0π+) B(Σ+π0) B(Σ+π+π−) B(Σ+ω) NΛ+ cΛ−c 1 −0.80 −0.71 −0.55 −0.42 −0.43 −0.68 −0.64 −0.48 −0.57 −0.46 −0.51 −0.21 B(pK0 S) 1 0.69 0.52 0.47 0.47 0.59 0.56 0.50 0.51 0.41 0.54 0.23 B(pK−π+) 1 0.57 0.73 0.84 0.64 0.61 0.70 0.54 0.42 0.80 0.37 B(pK0 Sπ 0) 1 0.42 0.47 0.43 0.43 0.40 0.37 0.32 0.47 0.21 B(pK0 Sπ +π− ) 1 0.70 0.42 0.42 0.54 0.36 0.26 0.63 0.29 B(pK−π+π0) 1 0.46 0.47 0.61 0.40 0.30 0.74 0.35 B(Λπ+) 1 0.65 0.57 0.57 0.34 0.49 0.21 B(Λπ+ π0) 1 0.56 0.57 0.36 0.50 0.22 B(Λπ+π−π+) 1 0.50 0.28 0.59 0.27 B(Σ0π+) 1 0.28 0.42 0.18 B(Σ+π0) 1 0.34 0.16 B(Σ+π+π−) 1 0.33 B(Σ+ω) 1
![TABLE III. Comparison of the measured BFs in this work with previous results from PDG [4]](https://thumb-eu.123doks.com/thumbv2/9libnet/4231469.66592/6.918.135.392.140.359/table-iii-comparison-measured-bfs-work-previous-results.webp)
